Szymon Rusinkiewicz

Efficient variants of the ICP algorithm

The ICP (Iterative Closest Point) algorithm is widely used for geometric alignment of three-dimensional models when an initial estimate of the relative pose is known. Many variants of ICP have been proposed, affecting all phases of the algorithm from the selection and matching of points to the minimization strategy. We enumerate and classify many of these variants, and evaluate their effect on the speed with which the correct alignment is reached. In order to improve convergence for nearly-flat meshes with small features, such as inscribed surfaces, we introduce a new variant based on uniform sampling of the space of normals. We conclude by proposing a combination of ICP variants optimized for high speed. We demonstrate an implementation that is able to align two range images in a few tens of milliseconds, assuming a good initial guess. This capability has potential application to real-time 3D model acquisition and model-based tracking.

The digital Michelangelo project: 3D scanning of large statues

We describe a hardware and software system for digitizing the shape and color of large fragile objects under non-laboratory conditions. Our system employs laser triangulation rangefinders, laser time-of-flight rangefinders, digital still cameras, and a suite of software for acquiring, aligning, merging, and viewing scanned data. As a demonstration of this system, we digitized 10 statues by Michelangelo, including the well-known figure of David, two building interiors, and all 1,163 extant fragments of the Forma Urbis Romae, a giant marble map of ancient Rome. Our largest single dataset is of the David - 2 billion polygons and 7,000 color images. In this paper, we discuss the challenges we faced in building this system, the solutions we employed, and the lessons we learned. We focus in particular on the unusual design of our laser triangulation scanner and on the algorithms and software we developed for handling very large scanned models.

Rotation invariant spherical harmonic representation of 3D shape descriptors

One of the challenges in 3D shape matching arises from the fact that in many applications, models should be considered to be the same if they differ by a rotation. Consequently, when comparing two models, a similarity metric implicitly provides the measure of similarity at the optimal alignment. Explicitly solving for the optimal alignment is usually impractical. So, two general methods have been proposed for addressing this issue: (1) Every model is represented using rotation invariant descriptors. (2) Every model is described by a rotation dependent descriptor that is aligned into a canonical coordinate system defined by the model. In this paper, we describe the limitations of canonical alignment and discuss an alternate method, based on spherical harmonics, for obtaining rotation invariant representations. We describe the properties of this tool and show how it can be applied to a number of existing, orientation dependent descriptors to improve their matching performance. The advantages of this tool are two-fold: First, it improves the matching performance of many descriptors. Second, it reduces the dimensionality of the descriptor, providing a more compact representation, which in turn makes comparing two models more efficient.

QSplat: a multiresolution point rendering system for large meshes

Advances in 3D scanning technologies have enabled the practical creation of meshes with hundreds of millions of polygons. Traditional algorithms for display, simplification, and progressive transmission of meshes are impractical for data sets of this size. We describe a system for representing and progressively displaying these meshes that combines a multiresolution hierarchy based on bounding spheres with a rendering system based on points. A single data structure is used for view frustum culling, backface culling, level-of-detail selection, and rendering. The representation is compact and can be computed quickly, making it suitable for large data sets. Our implementation, written for use in a large-scale 3D digitization project, launches quickly, maintains a user-settable interactive frame rate regardless of object complexity or camera position, yields reasonable image quality during motion, and refines progressively when idle to a high final image quality. We have demonstrated the system on scanned models containing hundreds of millions of samples.

Real-time 3D model acquisition

The digitization of the 3D shape of real objects is a rapidly expanding field, with applications in entertainment, design, and archaeology. We propose a new 3D model acquisition system that permits the user to rotate an object by hand and see a continuously-updated model as the object is scanned. This tight feedback loop allows the user to find and fill holes in the model in real time, and determine when the object has been completely covered. Our system is based on a 60 Hz. structured-light rangefinder, a real-time variant of ICP (iterative closest points) for alignment, and point-based merging and rendering algorithms. We demonstrate the ability of our prototype to scan objects faster and with greater ease than conventional model acquisition pipelines.

Modeling by example

In this paper, we investigate a data-driven synthesis approach to constructing 3D geometric surface models. We provide methods with which a user can search a large database of 3D meshes to find parts of interest, cut the desired parts out of the meshes with intelligent scissoring, and composite them together in different ways to form new objects. The main benefit of this approach is that it is both easy to learn and able to produce highly detailed geometric models -- the conceptual design for new models comes from the user, while the geometric details come from examples in the database. The focus of the paper is on the main research issues motivated by the proposed approach: (1) interactive segmentation of 3D surfaces, (2) shape-based search to find 3D models with parts matching a query, and (3) composition of parts to form new models. We provide new research contributions on all three topics and incorporate them into a prototype modeling system. Experience with our prototype system indicates that it allows untrained users to create interesting and detailed 3D models.

Estimating curvatures and their derivatives on triangle meshes

The computation of curvature and other differential properties of surfaces is essential for many techniques in analysis and rendering. We present a finite-differences approach for estimating curvatures on irregular triangle meshes that may be thought of as an extension of a common method for estimating per-vertex normals. The technique is efficient in space and time, and results in significantly fewer outlier estimates while more broadly offering accuracy comparable to existing methods. It generalizes naturally to computing derivatives of curvature and higher-order surface differentials.

Efficiently combining positions and normals for precise 3D geometry

Range scanning, manual 3D editing, and other modeling approaches can provide information about the geometry of surfaces in the form of either 3D positions (e.g., triangle meshes or range images) or orientations (normal maps or bump maps). We present an algorithm that combines these two kinds of estimates to produce a new surface that approximates both. Our formulation is linear, allowing it to operate efficiently on complex meshes commonly used in graphics. It also treats high-and low-frequency components separately, allowing it to optimally combine outputs from data sources such as stereo triangulation and photometric stereo, which have different error-vs.-frequency characteristics. We demonstrate the ability of our technique to both recover high-frequency details and avoid low-frequency bias, producing surfaces that are more widely applicable than position or orientation data alone.

A planar-reflective symmetry transform for 3D shapes

Symmetry is an important cue for many applications, including object alignment, recognition, and segmentation. In this paper, we describe a planar reflective symmetry transform (PRST) that captures a continuous measure of the reflectional symmetry of a shape with respect to all possible planes. This transform combines and extends previous work that has focused on global symmetries with respect to the center of mass in 3D meshes and local symmetries with respect to points in 2D images. We provide an efficient Monte Carlo sampling algorithm for computing the transform for surfaces and show that it is stable under common transformations. We also provide an iterative refinement algorithm to find local maxima of the transform precisely. We use the transform to define two new geometric properties, center of symmetry and principal symmetry axes, and show that they are useful for aligning objects in a canonical coordinate system. Finally, we demonstrate that the symmetry transform is useful for several applications in computer graphics, including shape matching, segmentation of meshes into parts, and automatic viewpoint selection.

Geometrically stable sampling for the ICP algorithm

The iterative closest point (ICP) algorithm is a widely used method for aligning three-dimensional point sets. The quality of alignment obtained by this algorithm depends heavily on choosing good pairs of corresponding points in the two datasets. If too many points are chosen from featureless regions of the data, the algorithm converges slowly, finds the wrong pose, or even diverges, especially in the presence of noise or miscalibration in the input data. We describe a method for detecting uncertainty in pose, and we propose a point selection strategy for ICP that minimizes this uncertainty by choosing samples that constrain potentially unstable transformations.